Isothermal Adiabatic Processes

8 MCQs3 revision cards9-step worked example

Source: NCERT ThermodynamicsPYQ coverage: NEET 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

The trap: On a P–V diagram, which curve is steeper — isothermal or adiabatic? Students routinely swap them. The adiabatic curve is always steeper than the isothermal at the same point. The slope ratio is γ (the adiabatic index, Cₚ/Cᵥ). This single confusion costs marks in graph-interpretation MCQs that appear roughly every 2–3 years.

Isothermal process. Temperature stays constant. For an ideal gas, PV = constant. All the heat supplied converts into work (ΔU = 0 because temperature doesn't change). Work done by the gas during isothermal expansion: W = nRT ln(V_f / V_i) (NCERT Class 11 Physics, Chapter 11, page 6). The process requires the system to exchange heat with a reservoir slowly enough to maintain thermal equilibrium — quasi-static by definition.

Adiabatic process. No heat exchange: Q = 0. The gas does work at the expense of its internal energy, so temperature changes. The governing relations are PVᵞ = constant and TVᵞ⁻¹ = constant (NCERT Class 11 Physics, Chapter 11, page 7). During adiabatic expansion the gas cools; during adiabatic compression it heats up.

Why the adiabat is steeper. Differentiate PV = const → dP/dV = −P/V. Differentiate PVᵞ = const → dP/dV = −γP/V. Since γ > 1 for all ideal gases, the adiabatic slope magnitude is γ times the isothermal slope at the same (P, V) point. Memorise: "adiabatic angles down sharper."

Watch-out for NEET: When a P–V diagram shows two curves through the same initial state, the steeper one is adiabatic. If the question asks which process does more work between the same initial and final volumes, compare the areas — the isothermal curve lies above the adiabat during expansion, so isothermal work > adiabatic work for the same volume change.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

In an isothermal process involving an ideal gas, which quantity remains constant?

MCQ 2Easy RecallPractice

In an adiabatic process, which of the following is true?

MCQ 3Easy RecallPractice

Which equation governs an isothermal process for an ideal gas?

MCQ 4Direct ApplicationPractice

Two moles of an ideal gas expand isothermally at 300 K from volume V to 2V. The work done by the gas is:

MCQ 5Direct ApplicationPractice

On a P–V diagram, an isothermal and an adiabatic curve pass through the same point. At that point, the ratio of the magnitude of the adiabatic slope to the isothermal slope is:

MCQ 6Direct ApplicationPractice

An ideal gas undergoes adiabatic expansion. Which of the following correctly describes the changes in temperature and internal energy?

MCQ 7Concept TrapPractice

An ideal gas is compressed from volume V₁ to V₂ (V₂ < V₁) first isothermally and then adiabatically. In which process is the magnitude of work done by the gas greater?

MCQ 8Direct ApplicationPractice

During isothermal expansion of an ideal gas, the heat absorbed by the gas is:

Quick recall before you leave

Worked Example

1
Given
- Initial state: (P₀, V₀) for both processes - Final volume: 2V₀ - Curve A: PV = constant - Curve B: PVᵞ = constant, γ = 1.4
2
Required
(a) Identify which curve is isothermal and which is adiabatic. (b) Determine which process has greater work done by the gas.
3
Concept
Isothermal: PV = constant (Boyle's law at constant T). Adiabatic: PVᵞ = constant (no heat exchange). The adiabatic curve is steeper — its slope magnitude is γ times the isothermal slope at any common (P, V) point. During expansion to the same final volume, the isothermal curve lies above the adiabat, enclosing more area.
4
Formula
Isothermal work: W_iso = nRT ln(V_f / V_i) Adiabatic: PVᵞ = constant governs the curve shape.
5
Substitution
Both curves start at (P₀, V₀) and end at volume 2V₀. For the isothermal curve, final pressure: P_f = P₀V₀ / (2V₀) = P₀/2. For the adiabatic curve, final pressure: P_f = P₀(V₀/2V₀)ᵞ = P₀ / 2^1.4 = P₀ / 2.639.
6
Calculation
Since P₀/2 > P₀/2.639, the isothermal curve has a higher final pressure than the adiabatic curve at the same volume 2V₀. This means the isothermal curve lies above the adiabat throughout the expansion. The area under the P–V curve (which equals the work done) is larger for the isothermal process. Note: γ = 1.4 is exact (given in the problem). The value 2^1.4 ≈ 2.639 uses the exact exponent; the decimal is for comparison purposes.
7
Final answer
(a) Curve A (PV = constant) is the isothermal process; Curve B (PVᵞ = constant) is the adiabatic process. (b) The gas does more work during the isothermal expansion (larger area under the P–V curve).
8
Common trap
Swapping which curve is steeper. The adiabat drops more steeply because its slope is −γP/V compared to −P/V for the isotherm. Students who think the adiabat is flatter will incorrectly conclude adiabatic work > isothermal work for expansion.
9
Similar NEET-style question
"An ideal monoatomic gas (γ = 5/3) expands from state (P₁, V₁) to volume 3V₁ via (i) an isothermal process and (ii) an adiabatic process. In which case is the final pressure higher? In which case does the gas do more work?" (Answer: isothermal final pressure is higher; isothermal work is greater.) ---

Before solving, remember these

Definition

Isothermal process

Process at constant temperature. For ideal gas: ΔU = 0, so Q = W. Work done: W = nRT ln(V_f/V_i).

-- NCERT, p. 6

Definition

Adiabatic process

Process with no heat exchange (Q = 0). For ideal gas: PV^γ = constant, where γ = C_p/C_v. Also TV^(γ-1) = const and TP^((1-γ)/γ) = const. ΔU = -W; system cools when expanding adiabatically.

-- NCERT, p. 7

Formulas

4 formulas — click to collapse

Adiabatic relations for ideal gas

P V^{γ} = const; T V^{γ - 1} = const

Relations holding during reversible adiabatic process. gamma = Cp/Cv.

Symbol	Quantity	SI Unit
P	pressure	Pa
V	volume	m^3
T	temperature	K
gamma	adiabatic index	-

Valid when

Q = 0 (no heat exchange)
Quasi-static (reversible)
Ideal gas

First law of thermodynamics

Δ U = Q - W

Change in internal energy = heat ADDED minus work DONE BY the system. Energy conservation including thermal energy.

Symbol	Quantity	SI Unit
Delta_U	change in internal energy	J
Q	heat added to system	J
W	work done BY system	J

Valid when

Closed system (no mass exchange)
Sign convention: Q>0 heat in, W>0 system does work

Work done in isothermal process (ideal gas)

W = n R T ln \frac{V _{f}}{V _{i}}

Work done by ideal gas during isothermal expansion. Q = W (since Delta_U = 0). Reverse for compression.

Symbol	Quantity	SI Unit
n	moles	mol
R	gas constant 8.314	J/mol/K
T	temperature	K
V_i, V_f	initial/final volume	m^3

Valid when

Ideal gas
Quasi-static (reversible) isothermal

Mayer's relation (Cp - Cv = R)

C_{p} - C_{v} = R

For ideal gas: difference of molar specific heats equals gas constant R. Useful for converting between Cp and Cv.

Symbol	Quantity	SI Unit
Cp	molar specific heat at const P	J/mol/K
Cv	molar specific heat at const V	J/mol/K
R	8.314	J/mol/K

Valid when

Ideal gas
Per mole basis

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

2 items — click to collapse

Trap

Adiabatic vs isothermal P-V curve

Category: Graph Interpretation

Student misidentifies which P-V curve is adiabatic (steeper) vs isothermal.

When it triggers

P-V graph showing one or more processes; question asks for process type.

How to avoid

Adiabatic curve is STEEPER than isothermal at the same point (slope ratio = γ). Adiabat: PV^γ; isotherm: PV = const.

Mistake

Identifies adiabatic curve as gentler than isothermal on P-V diagram (or vice versa).

Root cause: graph misread

Correction

Adiabatic curve is STEEPER than isothermal at the same P-V point. Slope ratio at same point: adiabatic / isothermal = γ. Memorise: 'adiabatic angles down sharper'.

Past Year Questions

4 questions from NEET 2022, 2023, 2024, 2025. Answers verified against NTA official keys. — click to collapse

NEET 2025

A container has two chambers of volumes V 1 = 2 litres and V 2 = 3 litres separated by a partition made of a thermal insulator. The chambers contain n 1 = 5 and n 2 = 4 moles of ideal gas at pressures p 1 = 1 atm and p 2 = 2 atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of

11.8 atm

21.3 atm

31.6 atm

41.4 atm

NTA Answer: Option 3(final)

NEET 2024Revised key

A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is:

1Zero

230 J

3–90 J

4–60 J

NTA Answer: Option 1(revised_final)

NEET 2023

A Carnot engine has an efficiency of 50% when its source is at a temperature 327°C. The temperature of the sink is

115°C

2100°C

3200°C

427°C

NTA Answer: Option 4(final)

NEET 2022

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is

NTA Answer: Option 3(final)

How NEET usually asks this

2 recurring patterns from past papers — click to collapse

Cyclic process: net Q = net W (since Delta_U cycle = 0). Compute work/heat over each segment.

Multi StepMedium

Common distractors

forgets net zero cycle

Computes only one segment's W

Identify P-V diagram or temperature behaviour of isothermal vs adiabatic process. Adiabatic: PV^gamma; isothermal: PV.

InterpretationMedium

Common distractors

swaps adiabatic isothermal curves

Confuses which curve is steeper

Sources

NCERT refs: Class 11 Physics Chapter 11, p.6 | Class 11 Physics Chapter 11, p.7

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Isothermal Adiabatic Processes

Lesson

Practice MCQs

Quick recall before you leave

W = nRT ln(V_f / V_i)

PVᵞ = constant; TVᵞ⁻¹ = constant

ΔU = Q − W

Worked Example

Before solving, remember these

Isothermal process

Adiabatic process

Formulas

Adiabatic relations for ideal gas

Valid when

First law of thermodynamics

Valid when

Work done in isothermal process (ideal gas)

Valid when

Mayer's relation (Cp - Cv = R)

Valid when

Exam Traps & Common Mistakes

Adiabatic vs isothermal P-V curve

When it triggers

How to avoid

Identifies adiabatic curve as gentler than isothermal on P-V diagram (or vice versa).

Correction

Past Year Questions

How NEET usually asks this

Cyclic process: net Q = net W (since Delta_U cycle = 0). Compute work/heat over each segment.

Common distractors

Identify P-V diagram or temperature behaviour of isothermal vs adiabatic process. Adiabatic: PV^gamma; isothermal: PV.

Common distractors

Sources

Free NEET study resources